MAT 1235 Calculus II Section 8 5 Probability

MAT 1235 Calculus II Section 8. 5 Probability http: //myhome. spu. edu/lauw

HW l l l Web. Assign 8. 5 Additional HW at the end of this PPT Quiz

Preview l Provide a 30 -minute snapshot of probability theory and its relationship with integration.

Preview l l l Provide a 30 -minute snapshot of probability theory and its relationship with integration. Engineering: MAT 2200 (3) Math major/minor: MAT 3360 (5)

Random Variables l Variables related to random behaviors

Example 1 l

Continuous Random Variables l Take range over an interval of real numbers.

Probability… of an event = the chance that the event will happen

Example 2 l

Probability… …of an event = the chance that the event will happen …is always between 0 and 1.

Example 3 l

Probability Density Function l

Probability Density Function Properties:

Example 4 l

Example 4 l

Average Value of a pdf l

Example 4 l

Exponential Distribution l

Example 5 The customer service at AT&T has an average waiting time of 2 minutes. Assume we can use the exponential distribution to model the waiting time. Find the probability that customer will be served within 5 minutes.

Example 5 l

Remarks l If a random variable is not given, be sure to define it.

Additional HW A type of light bulb is labeled as having an average lifetime of 1000 hours. It's reasonable to model the probability of failure of these bulbs by an exponential density function with mean μ = 1000. (a) Use this model to find the probability that a bulb fails within the first 200 hours. Give your answer correct to three decimal places. (b) Use this model to find the probability that a bulb burns for more than 800 hours. Give your answer correct to three decimal places. Answers: (a) 0. 181 (b) 0. 449